Yb∶KGW激光晶体无热方向的计算与分析

针对各向异性Yb∶KGW激光晶体有可能存在热透镜效应为零的传播方向（即无热方向），利用Biswal等人2篇文献和Pujol等人对Yb∶KGW晶体热膨胀系数的测量结果，分别采用最小二乘法和二阶张量旋转计算出对应晶体的热膨胀张量，据此计算出2篇文献中所述晶体的无热方向。通过对比分析发现：尽管晶体热膨胀张量存在一定的个体差异，但是该晶体普遍只存在2个无热方向，即当光为m偏振时，在p-g平面内与p轴成正负二十多度的2个方向，而不是Biswal等人给出的4个无热方向。另外，利用得到的热膨胀张量计算出某特定方向的热光特性与瑞典的Hellstrom等人报道的激光器热透镜实验结果相一致。

Calculation and analysis of athermal directions of Yb: KGW laser crystal

The anisotropic Yb∶KGW laser crystal may have the zero thermal lens effect in some propagation directions,according to the measurement results of Biswal et al and Pujol et al. The thermal expansion tensors of Yb∶KGW crystals mentioned in these two references were obtained by least square and tensor rotation methods respectively. And the athermal directions were calculated on the basis of the thermal expansion tensors. The comparison and analysis show that,although there is some difference between individual crystals,this kind of crystals generally has only two athermal directions instead of four athermal directions calculated by Biswal et al,that is to say,the angles between these two athermal directions and p axis are around ±20°in the p-g plane when light is polarized in m direction. Besides,the calculated thermo-optic properties in certain directions with thermal expansion tensor taken into account are consistent with the laser thermal lensing experimental results reported by Swedish Hellstrom et al.